[amp_mcq option1=”< 50%" option2="50%" option3="75%" option4="100%" correct="option1"]
The correct answer is A. < 50%.
A normal distribution is a probability distribution that is symmetrical about the mean, with the mean, median, and mode all being equal. The standard deviation is a measure of how spread out the data is, and it is calculated by taking the square root of the variance.
In a normal distribution, 68% of the data will fall within 1 standard deviation of the mean, 16% of the data will fall below 1 standard deviation below the mean and 16% of the data will fall above 1 standard deviation above the mean. 95% of the data will fall within 2 standard deviations of the mean, 2.5% of the data will fall below 2 standard deviations below the mean and 2.5% of the data will fall above 2 standard deviations above the mean. 99.7% of the data will fall within 3 standard deviations of the mean, 0.15% of the data will fall below 3 standard deviations below the mean and 0.15% of the data will fall above 3 standard deviations above the mean.
In this case, the mean is 1000 mm and the standard deviation is 200 mm. Therefore, 68% of the annual precipitation data will fall between 800 mm and 1200 mm. 16% of the annual precipitation data will fall below 800 mm and 16% of the annual precipitation data will fall above 1200 mm. 2.5% of the annual precipitation data will fall below 600 mm and 2.5% of the annual precipitation data will fall above 1400 mm. 0.15% of the annual precipitation data will fall below 400 mm and 0.15% of the annual precipitation data will fall above 1600 mm.
The probability that the annual precipitation will be more than 1200 mm is therefore less than 50%.